"Everyone wanted to have someone's head on a plate and now they do," said Brian Kleinhanzl, an analyst at financial services firm Keefe, Bruyette & Woods. "Now that he's gone, you go on to the next discussion."

Three issues will be taking center stage not only for Wells Fargo but also the $16 trillion U.S. banking industry: whether to start breaking up the big Wall Street institutions; separating the roles of chairman and CEO; and corporate governance rules that allow a bank chief executive who's under fire to walk away relatively unscathed outside of reputational damage.

Andrew Harrer | Bloomberg | Getty Images

John Stumpf, chief executive officer of Wells Fargo & Co., center, exits the Rayburn House Office building after a House Financial Services Committee hearing in Washington, D.C., U.S., on Thursday, Sept. 29, 2016.

Of the three, separating the chairman and CEO roles is the easiest.

There already has been pressure to strip JPMorgan Chase chief Jamie Dimon of the roles, though the move ultimately was unsuccessful. However, the Stumpf case could provide additional momentum.

"That is a great idea. I think we'll see additional pressure on all the banks to do that," said Erik Oja, equity analyst at CFRA. "Most U.S. banks do combine the two positions, which is rare. If you look globally, you see there's a strict separation of chairman and CEO."

Breaking up the banks, though, isn't as simple as breaking up job titles.

Though populists have been calling for dicing up the Wall Street power brokers since the crisis, there's been no progress made in that regard. While Dodd-Frank regulations have restricted how banks can operate, the big four — JPMorgan, Wells Fargo, Bank of America and Citigroup — have gotten only bigger and now control nearly half the assets of the entire U.S. banking system.